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<title>算法提高 拼图</title>
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 <p class="NOI"><span style="font-family:黑体;mso-ascii-font-family:Arial;
mso-ascii-theme-font:major-latin;mso-hansi-font-family:Arial;mso-hansi-theme-font:
major-latin">【问题描述】</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">给出一个</span><span lang="EN-US">n</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">&times;</span><span lang="EN-US">m</span><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">的方格图，现在要用如下</span><span lang="EN-US">L</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">型的积木拼到这个图中，使得方格图正好被拼满，请问总共有多少种拼法。其中，方格图的每一个方格正好能放积木中的一块。积木可以任意旋转。</span></p>
<p class="NOI0"><img src="http://lx.lanqiao.cn/RequireFile.do?fid=NemE2TeN" width="106" height="106" alt="" /></p>
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</v:shape><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI"><span style="font-family:黑体;mso-ascii-font-family:Arial;
mso-ascii-theme-font:major-latin;mso-hansi-font-family:Arial;mso-hansi-theme-font:
major-latin">【输入格式】</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">输入的第一行包含两个整数</span><span lang="EN-US">n, m</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">，表示方格图的大小。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI"><span style="font-family:黑体;mso-ascii-font-family:Arial;
mso-ascii-theme-font:major-latin;mso-hansi-font-family:Arial;mso-hansi-theme-font:
major-latin">【输出格式】</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">输出一行，表示可以放的方案数，由于方案数可能很多，所以请输出方案数除以</span><span lang="EN-US">1,000,000,007</span><span style="font-family:宋体;mso-ascii-font-family:
&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">的余数。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI"><span style="font-family:黑体;mso-ascii-font-family:Arial;
mso-ascii-theme-font:major-latin;mso-hansi-font-family:Arial;mso-hansi-theme-font:
major-latin">【样例输入】</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI1"><span lang="EN-US">6 2<o:p></o:p></span></p>
<p class="NOI"><span style="font-family:黑体;mso-ascii-font-family:Arial;
mso-ascii-theme-font:major-latin;mso-hansi-font-family:Arial;mso-hansi-theme-font:
major-latin">【样例输出】</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI1"><span lang="EN-US">4<o:p></o:p></span></p>
<p class="NOI"><span style="font-family:黑体;mso-ascii-font-family:Arial;
mso-ascii-theme-font:major-latin;mso-hansi-font-family:Arial;mso-hansi-theme-font:
major-latin">【样例说明】</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">四种拼法如下图所示：</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><img src="http://lx.lanqiao.cn/RequireFile.do?fid=dgDJLgJ9" width="454" height="278" alt="" /></p>
<p class="NOI0">&nbsp;</p>
<p class="NOI0"><!--[if mso & !supportInlineShapes & supportFields]><span
lang=EN-US><span style='mso-element:field-begin;mso-field-lock:yes'></span><span
style='mso-spacerun:yes'> </span>SHAPE <span
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<p class="NOI"><span style="font-family:黑体;mso-ascii-font-family:Arial;
mso-ascii-theme-font:major-latin;mso-hansi-font-family:Arial;mso-hansi-theme-font:
major-latin">【评测用例规模与约定】</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">在评测时将使用</span><span lang="EN-US">10</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">个评测用例对你的程序进行评测。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">评测用例</span><span lang="EN-US">1</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">和</span><span lang="EN-US">2</span><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">满足：</span><span lang="EN-US">1&lt;=n&lt;=30</span><span style="font-family:宋体;mso-ascii-font-family:
&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">，</span><span lang="EN-US">m=2</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">评测用例</span><span lang="EN-US">3</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">和</span><span lang="EN-US">4</span><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">满足：</span><span lang="EN-US">1&lt;=n, m&lt;=6</span><span style="font-family:宋体;mso-ascii-font-family:
&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">评测用例</span><span lang="EN-US">5</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">满足：</span><span lang="EN-US">1&lt;=n&lt;=100</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">，</span><span lang="EN-US">1&lt;=m&lt;=6</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">评测用例</span><span lang="EN-US">6</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">和</span><span lang="EN-US">7</span><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">满足：</span><span lang="EN-US">1&lt;=n&lt;=1000</span><span style="font-family:宋体;mso-ascii-font-family:
&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">，</span><span lang="EN-US">1&lt;=m&lt;=6</span><span style="font-family:宋体;mso-ascii-font-family:
&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="NOI0"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">评测用例</span><span lang="EN-US">8</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">、</span><span lang="EN-US">9</span><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">和</span><span lang="EN-US">10</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">满足：</span><span lang="EN-US">1&lt;=n&lt;=10^15</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">，</span><span lang="EN-US">1&lt;=m&lt;=7</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">。</span></p>
<p class="NOI0">&nbsp;</p>
<p class="NOI0"><span lang="EN-US"><o:p></o:p></span></p>